During the last session of the last day of the LIDS Paths Ahead Symposium, Sanjeev Kulkarni stepped up to the podium. The Kirsch Auditorium was full of current and former LIDS students, researchers, and professors from the Laboratory—all interested in discussing the future of research in information and decision systems. Sanjeev, a LIDS graduate and current professor of electrical engineering at Princeton University, gave a brief talk on some suggested next steps in problems of estimation, inference, and learning. As he finished reading the summary on the final slide of his presentation, a smile crept into Sanjeev's voice. "The last point I want to make is already up here," Sanjeev said, referring to the projection screen behind him, "But you'd need some pattern recognition to notice it." As he spoke, the first letter of each line on the summary slide grew larger and flashed red, spelling out SANJOY—the first name of the man who had been Sanjeev's academic advisor when he studied at LIDS more than twenty years ago. The audience burst into laughter. "I can't help but take this as an opportunity to express my gratitude for Sanjoy and all he's done," said Sanjeev. Animated fireworks burst onto the screen, eliciting another peal of laughter as the virtual explosions framed a picture of Sanjoy Mitter. "I had the good fortune to have Sanjoy as an advisor, and over the years he's had a profound impact on my intellectual outlook, as an advisor, mentor, and as a friend." His former advisor officially retired in 2009, but Sanjeev is still benefiting from and expanding on ideas that he encountered under Sanjoy's mentorship. Thanks to his experience at LIDS, the senior professor from Princeton finds interesting mathematical challenges everywhere he looks.

When he first came to MIT, Sanjeev was working as a researcher at Lincoln Laboratory. By the time he decided to complete a Ph.D. at the Institute, he had full financial support from Lincoln. Sanjeev was free to find a lab that fit his interests, rather than worrying about who had funding. "I think that I was drawn to LIDS because of the style of work," said Sanjeev, "I like understanding a problem very fundamentally and generally if possible. And yet I like to be grounded in application. I'm not a pure mathematician. I'm sort of a…theoretical engineer, if you will. LIDS was the natural home for me." Working with Sanjoy, Sanjeev said, was also a natural choice. Both student and professor were drawn to the beauty of theoretical formulation and driven by the challenge of creating targeted solutions for specific applications. Sanjeev's thesis grew into a collection of ideas and papers on computer vision and machine learning—two topic areas that were the subject of much attention at the time. "The nice thing about Sanjoy was that he was supportive of almost anything as long as it was meaningful, deep, and a new contribution," said Sanjeev. "Sometimes the best theoretical problems come from trying to understand an application," said Sanjeev. "[Other times] I'm just drawn to the beauty of some theoretical formulation because it's interesting in and of itself—mathematically it's elegant... Sometimes [solutions to those elegant problems] find lots of applications. Sometimes not right away, sometimes decades or even a hundred years later."

But as a professor Sanjeev said he's able to take the long view on such issues. He doesn't have to produce results in the next quarter. Instead, he contributes mathematically interesting solutions and draws connections within his field and between his discipline and other areas of study: He taught a course for the Operations Research and Financial Engineering department and collaborated with Princeton philosopher Gilbert Harman on a course on machine learning and epistemology. In his own lab, Sanjeev is working on a number of projects, but most recently he's been wrestling with understanding the inner workings of distributed systems. Distributed systems come in all shapes and sizes—communication networks, sensor networks, and even social networks. Sanjeev has been working with the psychology department at Princeton to understand more about how distributed decision-making works in human systems. "There are often problems in aggregating judgments from human experts," said Sanjeev, "They usually disagree. Sometimes these experts aren't even coherent within their own statements—they assign probabilities to events that don't satisfy the laws of probability. And yet they have useful information. So how do you extract wisdom from crowds?" Traditionally, decision makers might ask a panel of experts to make predictions about the probability of certain events occurring in a complex situation. For example, what if a decision maker asked a panel of experts to predict the chance that there will be a decline in surface water quality, or the extinction of certain wetland species, if the sea level rises by a certain amount. If the experts all respond with mathematically coherent answers to all the questions—if they all answer the question with a simple number—a decision maker can average the results and understand the advice of the expert panel. But if any of the experts decide that they can't answer all of the questions, or if they offer probabilities that don't add up, simply averaging the answers won't work. Sanjeev and his collaborators created a mathematical tool that builds on previous work in the field. The method offers a more versatile approach to aggregating the opinions of an expert panel, even in a scenario where members of the panel offer incomplete answers. Constraints—like incomplete information and nonsensical answers in the case of decision aggregation, or power, time, and computational limitations—make simple examples into complicated, interesting ones, said Sanjeev. Working within the bounds of those restrictions also moves the problem out of the idealized realm of infinite resources and unrealistic expectations and into the world of useful applications.

"One of the hardest parts of research is formulating the right question—questions that are deep, meaningful, will be a contribution, but that you can make some headway on," said Sanjeev, "If you ask the right questions then usually good things will follow."
Finding the time to shoulder all of the responsibilities associated with being a professor, researcher, and mentor is also a challenge. But, just as in the case of toiling away at a difficult but meaningful problem, good things follow from putting work into your students. "At the beginning, they don't have a real sense of what this whole enterprise is about, or how to do research. By the end, they're leaving as colleagues. … I love it when a student is about to graduate, or is in the last year of their Ph.D. program," said Sanjeev, "By that point they're coming to me and saying, 'Hey I just found this interesting paper. Here's what I think is an interesting problem. What do you think?'" Seeing researchers make that transition from student to colleague is incredibly rewarding, and Sanjeev can't help but connect that to his own experience, when he was developing as a young academic in the invigorating LIDS environment. "We would often eat lunch in the reading room, surrounded by LIDS technical reports," Sanjeev recalled, "Once in a while, if no one else was in there, I'd wander around and pick up some of [the reports] and just see really interesting work. You'd see names that you'd recognize. Names you know passed through there. A lot of the interactions, and often the most meaningful ones, just happened as a matter of course. It's not preplanned. You just bump into someone, have a conversation and it leads to something interesting...If you apply yourself and enjoy yourself you'll get something really profound out of your LIDS experience."